Provides examples which suggest the importance of giving children opportunities to create their own arguments and of allowing them the opportunity to verbalize these arguments in clinical interviews. Also indicates that if time is spent interviewing children individually, instruction can be matched to the way they think. (JN)

Instruction in estimation is proposed as a natural context to develop and practice important thinking skills. These skills are described and estimation activities are proposed for each. (MNS)

Indicates how thinking strategies help children learn the basic facts for whole numbers, listing several strategies involved in addition, subtraction, multiplication, and division. Also lists books and articles for illustrations of the strategies and how to teach them, and two sources for research findings on thinking strategies for basic facts.…

Two computer games, Guess and Rule, can be used to improve students' thinking strategies. BASIC and Logo programs are given for each game, and facts and additional references are included. (MNS)

Concerns about how mathematics should be taught are discussed. Considered are operational and conceptual domains of thought, with many explicit examples. Educational implications, with premises, are noted, and an alternative is described. (MNS)

The problem-solving strategy "look for a pattern" is explored. The staircase problem and the region problem are discussed in detail, with varying solution procedures, and three other problem activities are outlined. (MNS)

Presents two seasonally related investigations involving arithmetic series to develop critical thinking: (1) the number of candles needed for the eight nights of Hanukkah, and (2) the number of presents given during "The Twelve Days of Christmas." Students also calculated the amount of money needed to buy all the presents. (MDH)

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Explores three questions related to the kindergarten mathematics curriculum: (1) How much do young students' limited abilities to process information hamper performance on worksheet tasks? (2) How is mathematics currently taught in kindergarten? and (3) What materials and activities are appropriate for mathematics learning in kindergarten? (MDH)

Presents a 6-day unit for grades 2-4 to enable students to understand the concept of time and how the analog clock works. Using concrete materials and cooperative learning, the unit presents cognitive, affective, and psychomotor objectives and activities for each lesson. (MDH)

The history of mental computation in the elementary school curriculum is briefly described, followed by discussion of the benefits of mental computation. How thinking skills are enhanced is then illustrated. (MNS)

Questions about teaching rational numbers are discussed, dealing with when to teach the meaning of fractions and of decimals, when and how to teach computation with fractions and with decimals, and other issues. (MNS)

Division of fractions and division of decimals, both troublesome, are discussed in relation to helping students learn well and retain what they have learned. A strong conceptual base, mastery of related concepts and skills, and meaningful development are stressed. (MNS)

Increasing the amount of problem-solving training in the preservice education of mathematics teachers is promoted. Such problems should be designed to help preservice teachers acquire an "open search" frame of mind, according to the authors. (MP)